We demonstrate that an exotically chiral
f-wave topological superfluid can be induced in cold-fermionic-atom triangular optical lattices through a laser-field-generated effective non-Abelian gauge field, controllable Zeeman fields, and
s-wave Feshbach resonance. We find that the chiral
f-wave topological superfluid is characterized by three gapless Majorana edge states located on the boundary of the system. More interestingly, these Majorana edge states degenerate into one Majorana fermion bound to each vortex in the superfluid. Our proposal enlarges the topological superfluid family and specifies a unique experimentally controllable system to study Majorana fermion physics.